Abstract:
We classify compact simply-connected 5-dimensional manifolds which admit a metric of nonnegative curvature with a connected non-abelian group acting by isometries. We show that they are diffeomorphic to either S^5, S^3 x S^2, the nontrivial S^3-bundle over S^2 or the Wu-manifold, SU(3)/SO(3). This result is a consequence of our equivariant classification of all SO(3) and SU(2)-actions on compact simply-connected 5-manifolds. In the case of positive curvature we obtain a partial classification.

Abstract:
We prove the hydrodynamic limit for a particle system in which particles may have different velocities. We assume that we have two infinite reservoirs of particles at the boundary: this is the so-called boundary driven process. The dynamics we considered consists of a weakly asymmetric simple exclusion process with collision among particles having different velocities.

Abstract:
management plan is a technical document that establish zoning and rules that will define the protect area usage and its natural resources management. in 1979 they were legally established in brazil aiming to adapt and orientate the ecological handling of national parks, which are still not fully implemented. this indicates the necessity of carrying out the zoning as a base to the protected territory planning. however, preparation and implementation process of this document was extremely varied and suffered several modifications aiming its improvement. the objective of this work was to analyze the evolution of management plans in the context of national parks management, analyzing as a concrete case its implementation in the state of rio de janeiro, brazil. the preparation of management plans for brazilian parks was marked by the existence of three different methodological references that was reflected in the variety of plans identified for five national parks studied here (itatiaia np, serra dos órg？os np, tijuca np, serra da bocaina np and restinga da jurubatiba np). as a general pattern, the plans were neither prepared nor revised with the periodicity established by the legislation. this shows a difficulty in the implementation of this instrument even almost thirty years after its institution.

Abstract:
This study aimed to verify how the franchisor combines control and strategic flexibility, identifying control systems it uses to monitor, measure, assess uncertainty, validate strategies, promote change, strategic initiatives to emerge and contribute to the learning network in order continuous improvement of the competitive position of the franchise. The theoretical framework was to support the relationship between franchiser and franchisee proposed in the literature, transaction costs, the agency theory and management control systems defined and categorized by Simons (1994). To fulfill the objective proposed, we used the exploratory research and the strategy of a single case study with unit of analysis in the field of Marketing and Sales of a franchisor. The data collection instrument was a semi-structured interview with four executives, chosen because of the topics. Through the identification of interactive control systems used by the franchisor, it was found that it adds in the strategic management of the franchise, the management approaches to minimize costs and maximize opportunities, combining control and strategic flexibility. O presente estudo objetivou verificar como o franqueador alia controle e flexibilidade estratégica, identificando os sistemas de controle que utiliza para monitorar, mensurar, avaliar incertezas, validar estratégias, promover mudan as, fazer emergir iniciativas estratégicas e contribuir com o aprendizado da rede, tendo em vista a melhoria contínua da posi o competitiva da franquia. O referencial teórico teve como suporte o relacionamento entre franqueador e franqueado proposto na literatura, os custos de transa o, a teoria de agência e os sistemas de controle administrativo definidos e categorizados por Simons (1994). Visando o cumprimento do objetivo proposto, utilizou-se a pesquisa do tipo exploratória e a estratégia de estudo de caso único tendo como unidade de análise a área de Marketing e Vendas de uma franqueadora. O instrumento de coleta de dados foi a entrevista semi-estruturada realizada com 4 executivos da área, escolhidos em raz o dos temas pesquisados. Através da identifica o dos sistemas de controle interativo utilizados pela franqueadora, verificou-se que ela agrega na administra o estratégica da franquia, as abordagens gerenciais de minimiza o de custos e maximiza o de oportunidades, aliando controle e flexibilidade estratégica.

Abstract:
We propose and analyze a stochastic model which explains, analytically, the cutoff behavior of real scale-free networks previously modeled computationally by Amaral et al. [Proc. Natl. Acad. Sci. U.S.A. 97, 11149 (2000)] and others. We present a mathematical model that can explain several existing computational scale-free network generation models. This yields a theoretical basis to understand cutoff behavior in complex networks, previously treated only with simulations using distinct models. Therefore, ours is an integrative approach that unifies the existing literature on cutoff behavior in scale-free networks. Furthermore, our mathematical model allows us to reach conclusions not hitherto possible with computational models: the ability to predict the equilibrium point of active vertices and to relate the growth of networks with the probability of aging. We also discuss how our model introduces a useful way to classify scale free behavior of complex networks.

Abstract:
To expand the toolbox available to network science, we study the isomorphism between distance and Fuzzy (proximity or strength) graphs. Distinct transitive closures in Fuzzy graphs lead to closures of their isomorphic distance graphs with widely different structural properties. For instance, the All Pairs Shortest Paths (APSP) problem, based on the Dijkstra algorithm, is equivalent to a metric closure, which is only one of the possible ways to calculate shortest paths. Understanding and mapping this isomorphism is necessary to analyse models of complex networks based on weighted graphs. Any conclusions derived from such models should take into account the distortions imposed on graph topology when converting proximity/strength into distance graphs, to subsequently compute path length and shortest path measures. We characterise the isomorphism using the max-min and Dombi disjunction/conjunction pairs. This allows us to: (1) study alternative distance closures, such as those based on diffusion, metric, and ultra-metric distances; (2) identify the operators closest to the metric closure of distance graphs (the APSP), but which are logically consistent; and (3) propose a simple method to compute alternative distance closures using existing algorithms for the APSP. In particular, we show that a specific diffusion distance is promising for community detection in complex networks, and is based on desirable axioms for logical inference or approximate reasoning on networks; it also provides a simple algebraic means to compute diffusion processes on networks. Based on these results, we argue that choosing different distance closures can lead to different conclusions about indirect associations on network data, as well as the structure of complex networks, and are thus important to consider.

Abstract:
In this note, we prove a sharp $L^p$-rate of convergence of the number of upcrossings to the local time of the Brownian motion. In particular, it provides novel $p$-variation estimates ($2 < p < \infty$) for the number of upcrossings of the Brownian motion. Our result complements the fundamental work of Koshnevisan \cite{kho} who obtains an almost sure exact rate of convergence in the sup norm.

Abstract:
In this note, we establish a novel maximal inequality of the 2D Young integral $\int_a^b\int_c^d FdG$ in terms of the $(p,q)$-bivariation norms of the section functions $x\mapsto F(x,y)$ and $y\mapsto F(x,y)$ where $G:[a,b]\times [c,d]\rightarrow \mathbb{R}$ is a controlled path satisfying finite $(p,q)$-variation conditions. The proof is reminiscent from the Young's original ideas \cite{young1} in defining two-parameter integrals in terms of $(p,q)$-finite bivariations. Our result complements the standard maximal inequality established by Towghi \cite{towghi1} in terms of joint variations. We apply the maximal inequality to get novel strong approximations for 2D Young integrals w.r.t the Brownian local time in terms of number of upcrossings of a given approximating random walk.